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Mass spectrum at the collector plane for the sample being measured: ion current against position; grey lines = the Faraday cups
Histogram of fitted ages from repeated runs; the grey line is the true crystallisation age
Evolution of 87Sr/86Sr with time for each mineral: the lines fan out from the common initial ratio
Two-point age of each mineral with the whole rock; dashed lines = true age and heating-event age
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The science
Radiometric dating with an isochron. Rubidium-87 decays to strontium-87 (half-life about 49.8 billion years) with decay constant λ = 1.393×10-11 per year. Strontium-86 is stable and not produced by any decay, so it serves as a reference isotope. A mineral that crystallised t years ago with an initial ratio (87Sr/86Sr)0 has today
(87Sr/86Sr) = (87Sr/86Sr)0 + (87Rb/86Sr) · (eλt − 1)
That is a straight line in the plot of 87Sr/86Sr against 87Rb/86Sr. Minerals of one rock all start from the same initial ratio (Sr isotopes were mixed in the melt) but have very different Rb/Sr (biotite takes in Rb, plagioclase takes in Sr), so after time t they fan out along a line whose slope b = eλt − 1 gives the age, t = ln(1 + b)/λ, and whose intercept is the initial ratio. Because the age comes from the slope, no assumption about the initial ratio is needed, and a closed system proves itself by lying on a line. The lab fits the points with the York (1969) regression, which accepts errors in both coordinates, and reports the standard error of the slope and the MSWD (mean square of weighted deviates): MSWD near 1 means the scatter is explained by the stated errors, much larger means the minerals do not share one age.
Resetting. If the rock is reheated later, minerals whose Rb-Sr closure temperature (roughly biotite 300 C, K-feldspar 400 C, muscovite 500 C; approximate values) is below the peak temperature exchange strontium with the surrounding rock, which makes them lose their radiogenic 87Sr relative to the whole rock. Their two-point ages with the whole rock then give the age of the event, while high-closure minerals and the whole rock still carry the old age (graph 4). A fit through all points then has a large MSWD.
The mass spectrometer. Strontium is loaded on a filament, ionised by heat (thermal ionisation) and accelerated through a voltage V, so every Sr+ ion of mass m has speed √(2qV/m). In a uniform magnetic field B the force qvB bends the path on a circle of radius
r = (1/B) √(2mV/q)
so heavier isotopes bend less. In the 90 degree sector design the tuned field puts 87Sr on a radius of 0.240 m; 86Sr and 88Sr hit the collector plane about 3 mm to either side, where separate Faraday cups count them at the same time. If the field or voltage is off by a fraction of a percent the beams slide off the cups (use the detuning slider). The measured ratio is not the true one because lighter isotopes ionise and move a little differently: the instrumental bias follows the exponential law Rmeasured = Rtrue (mi/mj)β. It is removed by assuming that 86Sr/88Sr is always 0.1194, which fixes β; the page does exactly this correction.
Honest simplifications. (1) A closed whole-rock sample and six idealised mineral separates with round Rb/Sr values; real granites also have inherited components, partial reset and mixed ages. (2) Reset is modelled as full re-equilibration with the whole rock at the event age for the minerals below the peak temperature, a simplification of diffusion. (3) Ion optics use a sharp-edged uniform field with normal entrance (no fringe fields or lens focusing), and the 3D scene magnifies the beam separations for visibility. (4) Noise is Gaussian with the chosen precision; real data also include blank, interference by 87Rb and drifts. (5) The decay constant is a fixed round literature value that you can change; the choice of constant moves all ages by about 1 percent.
Checks run in the page. A noise-free isochron returns the input age; 300 repeated noisy runs show the scatter of the fitted ages agrees with the uncertainty the York fit reports and that the mean age is unbiased; the mass-bias correction returns the true ratio; the collector position from the closed-form geometry matches a Lorentz-force integration; and the total mass 87 (Rb plus Sr) is conserved in a closed mineral.